Shipboard gravimeter

ABSTRACT

A system for processing gravimeter signals obtained aboard a seagoing vessel is described which eliminates short term accelerations due to pitch, roll and heave of the vessel. This system compares the frequency of the output signal from a vibrating string accelerometer with the counted-down output of a voltage controlled oscillator set to the mean frequency of the accelerometer. The frequency difference of these two signals is converted into a voltage which is filtered by a low-pass filter to remove short term acceleration components and is then coupled to the voltage controlled oscillator. The output of this oscillator is thus locked onto only the low frequency components of the accelerometer and, as such, provides a signal whose frequency is proportional only to the local gravitational acceleration.

United States Patent [72] Inventors Charles G. Wing Ipswich; Robert W.Steer, Haverhill, both of, Mass. [2i] Appl, No. 849,665 r [22] FiledAug. 13, 1969 [45] Patented June 8, 1971 [73] Assignee The United Statesof America as represented by the Secretary of the Navy 7 [54] SHIPBOARDGRAVIMETER 7 Claims, 1 Drawing Fig.

[52] [1.8. CI 73/382, 73/517 [51] lnt.Cl 601v 7/16 [50] Field oiSearch..73/5l7 AV, 382

[56] References Cited UNITED STATES PATENTS 3,483,753 12/1969 LoebPrimarv ExaminerJames .I. Gill Attorneys-Rv I. Tompkins. L l Shrago andR. K. Tendler ABSTRACT: A system for processing gravimeter signalsobtained aboard a seagoing vessel is described which eliminates shortterm accelerations due to pitch, roll and heave of the vessel. Thissystem compares the frequency of the output signal from a vibratingstring accelerometer with the counteddown output ofa voltage controlledoscillator set to the mean frequency of the accelerometer. The frequencydifference of these two signals is converted into a voltage which isfiltered by a low-pass filter to remove short term accelerationcomponents and is then coupled to the voltage controlled oscillator. Theoutput of this oscillator is thus locked onto only the low frequencycomponents of the accelerometer and, as such, provides a signal whosefrequency is proportional only to the local gravitational acceleration.

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and heave of the vesselin which the gravity sensing accelerometer ismounted. Although much of this acceleration can be removed by mountingthe accelerometer on a gyrostabilized platform, further signalprocessing is necessary. Of the several types of gravity sensorsavailable, one of the most sensitive is the vibrating stringaccelerometer which produces a signal whose frequency is proportional tothe acceleration sensed. Although high frequency changes in the outputof this accelerometer can be filtered from the signal by low-passfilters, high frequency components are still present in the signal todegrade the gravity measurement.

The present invention utilizes a phase-lockedloop with a low-pass filterin its feedback path to eliminate more completely these high frequencycomponents. To accomplish this, the output of the accelerometer is fedto one input of a phase detector. At the same time, the output ofavoltage controlled oscillator is fed to the other input of thisdetector. The output of the detector is used to change the frequency ofthe voltage controlled oscillator until the output of the oscillator isexactly equal to the frequency of the accelerometer output, absent thosecomponents of the frequency due to short term variation. The short termcomponents are removed by filtering the output of the phase detector sothat the voltage controlling the oscillator does not contain short timeor high frequency variations present at the accelerometer output. Theoutput of the voltage controlled oscillator is thus proportional only tolong term accelerations, i.e., those due to a local gravitational force.The number of oscillations of the voltage controlled oscillator per unittime when registered in an appropriate digital counter is proportionalonly to the local gravitational field force.

It is therefore an object of this invention to provide a system foreliminating the high frequency components of the outputofa vibratingstring accelerometer.

Another object of the present invention is to provide adigital-to-analog recording system for measuring local gravitationalacceleration.

Other objects, advantages and novel features of the invention willbecome apparent from the following detailed description of the inventionwhen considered in conjunctiop with the accompanying drawing, the soleFIGURE of which illustrates a vibrating string accelerometer with animproved filter and readout means.

Referring to the sole FIGURE, a vibrating string accelerometer is shownenclosed in dotted box 1 with appropriate frequency multiplicationcircuits to increase its output frequency. The vibrating stringaccelerometer is connected to a phase-locked loop circuit shown enclosedin clotted box 2. Although accelerometer 1 may be any conventionalvibrating string accelerometer, a double vibrating string accelerometeris shown because ofits linearity. In general, the

output of a double vibrating string accelerometer is obtained byheterodyning the outputs of two vibrating strings. An accelerometer ofthis type is manufactured commercially by AMBAC Industries. The outputsof the two strings of this accelerometer are shown diagrammatically at 3and 4. The outputs of these strings are multiplied by equal amounts, M,by

age controlled oscillator set initially to deliver a square wave signalM times that ofthe signalfrom the vibrating string and a divide-by-Mcounter. The output of the phase detector controls the voltagecontrolled oscillator whose output is,divided by M and then returned toone of the inputs of thephase detector. The other input to the phasedetector is the sinusoidal signal from the vibrating string. When asignal is received from the vibrating string, it is converted to ahigher frequency M times that of the vibrating string signal by thevoltage controlled oscillator. This frequency is stepped down to thefrequency of the vibrating string and compared with the vibrating input.Subsequently, the oscillator is continually adjusted. The output of theoscillator is coupled to one of the inputs of heterodyning device 7 andrepresents an exact multiplication of the frequency of the vibratingstring. The outputs of these multipliers are heterodyned by conventionalcircuitry at 7 to yield a sinusoidal signal AF. The difference frequencyAF from the heterodyning detector is:

AF=M(K azK,AAzK AAQ2+K aA+) l where K, is a bias term and K is a scalefactor which is equal to the frequency response of the accelerometer perunit of gravitational acceleration sensed. To the extent to which thedouble string geometry is perfect, all even ordered terms approach zero,thus reducing the largest nonlinear term K When a double vibratingstring is used, calibration no longer requires a gravity range traversesince only a local value of gravity and the sum of the differencefrequency, 2K A+2KA 311 000, is needed to obtain the scale factor K toabout one part in I0 In one operating embodiment of this invention adouble vibrating string accelerometer had the following characteristics:

giants-inn 1 and 2 -i K Hz./G' 128 K2 Hz./G 0.001 K Hz./G 0.004 K Hz./G0.001

with an effective cross-axis sensitivity of l0" G/G and a temperaturecoefficient of 20 l0" G/C. It will be appreciated that AF of thisaccelerometer contains components which are proportional to the localgravitational field and miscellaneous short term accelerations. Theselatter accelerations are removed in the phase-locked loop section of thesubject signal processing circuit.

The phase-locked loop is composed of a voltage controlled oscillator 10,a countdown device 11, a phase detector 12 and a low-pass filter 13.

The output of accelerometer 1, AF, is the frequency which is to beduplicated by the counted-down component of the voltage controlledoscillator shown diagrammatically at 10. This oscillator generates asquare wave signal whose frequency is determined by a control voltage.The frequency of oscillator 10 is originally set at NAF so as to providea higher frequency output than is derivable from accelerometer 1. Itwill be appreciated that the higher the frequency of the oscillator themore precise will be the gravity measurement. In one embodiment theoriginal frequency of the oscillator was set to be 16 times that of themean output of the accelerometer. In order to facilitate a phasedetermination, a conventional frequency countdown counter 11 isemployed. This is a counter having a single pulsed output for every 16thsquare wave pulse from the oscillator. The output of counter 11 is oneof the inputs to phase detector 12. This phase detector may be anydevice which generates a voltage proportional to the phase differencebetween two input signals.

A conventional phase detector which can accommodate a sine wave and asquare wave at its input is described on page 74], FIGS. 19-20, ofPulse, Digital and Switching Waveforms," Jacob Millman and Herbert Taub,published by McGraw Hill, I965.

The phase detector used in one configuration has a-Iinear range of140961: radians.

The output of the phase detector controls oscillator 10 and completesthe phase-locked loop. in this loop is a low-pass filter 13 whichfilters from the output of detector 12 the aforementioned short termvariations in phase difference between (Fwd/N and \FY F therefore locksonto only the low frequency variations of AF. One way of describing theoperation of the phase-locked loop is to consider AF a constant carrierfrequency corresponding to the value of a local gravitational field witha varying modulation impressed thereon corresponding to theabove-mentioned short term variations. The phase-locked loop permits thevoltage controlled oscillator to lock onto the carrier frequency andthus produce a signal which is directly proportional to the value of thelocal gravitational field.

Low-pass filter 13 is set to have a cutoff frequency between 10 and 10"Hz. to eliminate accelerations due to Eotvos or fishtail variation,ship's heave and ship vibration. If an active analog filter system isused, the transfer function of the network employed is made toapproximate the desired low frequency response.

The filter in the phase-locked loop must meet three requirements: l Itshould separate signal and noise. Specifically, the signal at 10" Hz.should be attenuated by less than 3 db. (30 percent) and the noise at 10Hz. must be attenuated by more than 100 db. (I (2) Signals must not beamplified selectively at specific frequencies (the filter frequencyresponse must be flat in the passband). (3) Signals should not bedistorted excessively.

The second condition dictates a Butterworth" transfer function. Since aButterworth filter has a phase shift of 180 at the cutoff frequency f,,,for loop stability the phase-locked loop must be closed at a frequencylower than f Closing the loop atf ,,/2 ensures adequate stability. AButterworth filter I itself overshoots in its step response by 5 percentfor the second order and 8 percent for the third order. Addition of theclosed-loop damps the total response to prevent overshoot. Absence ofovershoot in the closed loop indicates an acceptable level of distortionof geophysical signals since a gravity step function is far worse thanany natural gravity signal.

Assuming a second order Butterworth filter we can find thehighest fwhich will satisfy our requirements The digital accumulator to bedescribed integrates the input frequency for seconds, effectivelyattenuating noise with a l0-second period by 14 db. An additional 86 db.attenuation is required from the second order Butterworth filter at fand the closed loop atf =f,,/2. The requiredf is 0.0045 H2.withf,,=0.004 Hz. and f =0.002 Hz., and the 1100 gal. heave isattenuated 104 db. to $0.6 mgal. The response time (the time required torespond 63 percent to a step input) is 160 seconds. Signals at 10 Hz.are attenuated by 1 db. (-10 percent).

Using a third order Butterworth, we have more latitude in pickingf,,.Withf,,=0.008 Hz. andf =0.004 Hz., heave is attenuated 106 db. to $0.5mgal., the response time is l 10 seconds and the 10 Hz. signal isattenuated by only 0.5 db. (=5 percent). The single practical advantageof the third order filter is in operations requiring frequent coursechanges. A course change results in a step change in the Eotvos inputand time required to settle to l mgal. is about 8 minutes for the secondorder and 5 minutes for the third order filter.

Choice of other low-pass filters having other transfer functions istreated in any textbook on linear circuit analysis. Active filters foruse in the subject system may be found in the Handbook of ActiveFilters" available from Burr-Brown Research Corporation I966).

The output of voltage controlled oscillator 10 can be shown to beF,,,,,=MN(K +K,G) (2) where this K 7 H2. in one application. This outputis coupled to a conventional digital accumulator 15 of the typemanufactured by Janus Control, Inc.

The accumulator registers the number of pulses generated by oscillator10 every l/(MNKn seconds so as to correspond to an equation giving thelocal gravitational field:

The accumulator is reset every l/(MNK seconds by a conventional resetpulse generator 16. This effectively divides by K, the number of pulsesproduced by oscillator 10. Equation (3) is derived from equation (2) andshows that the instantaneous value of the local gravitational field canbe automatically obtained as the output of the accumulator. In order tosubtract K IK, from (E K the accumulator is preset to a number equal toK /K by thumbwheel switches shown diagrammatically at 17. When thisnumber is preset in the accumulator, the accumulator must count K lKpulses from oscil lator 10 before a positive number is obtained as thecounter output. The number of pulses produced in the l/(MNK timeinterval is thus equal to the local value of G. If each of strings 3 and4 vibrates at approximately 9,300 Hz. and the difference between the twofrequencies, the scale factor, is 128 Hz./G plus a bias of 7 Hz.assuming that a phase-locked frequency multiplication by is performed onthe output of each string before heterodyning and a secondmultiplication by 16 is made to reach the oscillator frequency,

F l 1,200 Hz.+204,800 Hz. G/G.

Therefore, MNK =bias and MNK,=scale factor.

The output of digital accumulator 15 is converted to an analog signal bya conventional D/A converter 18. This signal may be coupled to any typeof display 20 capable of recording the amplitude of the analog signal asa function of time. Alternately, the count in the counter may be sampledat l/MNK second intervals and the count digitally recorded.

'What we claim is:

1. Apparatus for'removing short term frequency variations in the outputsignal from an accelerometer which is subjected to both steady and shortterm accelerations, which accelerometer is of the type which generatesan electrical signal having an instantaneous frequency proportional tothe acceleration to which it is subjected, comprising:

phase detection means having one of two input circuits coupled to theoutput of said accelerometer and having an output circuit at which isgenerated a signal having an amplitude proportional to the phasedifference between any pair of signals coupled to said input circuits;

an oscillator whose frequency is initially set to the mean frequency ofsaid accelerometer and is variable about said mean frequency in responseto the amplitude of a control voltage applied to a control circuitthereof, the output of said oscillator being coupled to the other inputcircuit of said phase detection means; and

means connected between the output circuit of said phase detection meansand the control circuit of said oscillator for coupling only lowfrequency components of the signal generated by said phase detectionmeans to said oscillator, whereby the frequency of said oscillator isproportional only to the steady accelerations to which saidaccelerometer is subjected.

2. Apparatus for providing an electrical signal whose frequency is apredetermined multiple of the frequency of that component of the outputsignal from a vibrating string accelerometer generated by the localgravitational field to which said accelerometer is subjected,comprising:

a phase detector having one of its two inputs coupled to the output ofsaid accelerometer and having an output circuit at which is generated asignal having an amplitude proportional to the phase difference betweenany pair of signals coupled to said inputs;

a voltage controlled oscillator having a center frequency equal to apredetermined multiple of the mean frequency of the output signal fromsaid accelerometer and having a control circuit which varies the outputfrequency of said amplitude of a control voltage applied thereto;

mined multiple; and means for coupling said last-mentioned signal to theother input of said phase detector so as to provide said detector with asecond input signal in addition to that supplied by said accelerometer,whereby the signal available at the output of said oscillator has afrequency which is proportional only to said local gravitationalacceleration. 3. A system for processing signals generated by avibrating string accelerometer and for determining the strength of thegravitational field to which said accelerometer is subjected,comprising:

a phase detector having one of its two inputs coupled to the output ofsaid accelerometer so as to provide said detector with a first inputsignal and having an output at which is provided a signal whoseamplitude represents the phase difference between any pair of signalscoupled to said inputs;

a voltage controlled oscillator for producing a pulsed output signalhaving a center frequency equal to N times the mean frequency of theoutput signal from said aecelerometer where N is a predeterminedpositive integer and having a control circuit which varies the outputfrequency of said oscillator about said center frequency in response tothe amplitude of a control voltage applied thereto;

means coupled to the output of said oscillator for producing a signal atits output which has a frequency exactly equal to the frequency of saidoscillator divided by N;

means for coupling the output of said last-mentioned means to the otherinput of said phase detector so as to provide said detector with asecond input signal;

a low-pass filter for attenuating the high frequency components of thesignal generated at the output of said phase detector;

means for connecting said low-pass filter between the output of saiddetector and the control circuit of said oscillator whereby only lowfrequency components of the signal from said detector are coupled tosaid oscillator; and

means for registering the number of output pulses generated by saidoscillator during a predetermined time interval, whereby said number isproportional to the gravitational field to which said accelerometer issubjected.

4. The apparatus as recited in claim 3 wherein said registering meansincludes:

the bias of said accelerometer divided by the scale factor of saidaccelerometer; and

means for periodically resetting said accumulator after a time periodequal to the reciprocal of N times said scale factor has elapsed,whereby the number accumulated in said accumulator during said timeperiod is equal to the gravitational acceleration to which saidaccelerometer is subjected.

5. A system for measuring local gravitational accelerations at seacomprising:

a vibrating string accelerometer which generates a first signal having afrequency proportional to accelerations to which it is subjected;

means for multiplying the frequency of said signal by a positiveinteger, M, so as to produce a second signal M times greater infrequency than said first signal;

a phase detector having one of its two inputs coupled to the output ofsaid multiplying means and having an output which provides a signalwhose amplitude represents the phase difference between signals coupledto said inputs;

a voltage controlled oscillator having a center frequency N times themean frequency output of said multiplying means and having a controlcircuit which varies the output frequency ofsaid oscillator about saidcenter frequency in response to the amplitude of a control voltageapplied thereto;

a low-pass filter;

means for connecting said low-pass filter between the output of saiddetector and the control circuit of said oscillator so as to complete afeedback loop to said oscillator which loop contains only low frequencycomponents of the signal from said detector;

divide-by-N means coupled between the output of said oscillator and theother input of said detector to provide said detector with a signalwhose frequency corresponds to that component of the frequency of saidsecond signal due only to gravitational accelerations; and

means coupled to the output of said oscillator for registering thenumber of oscillations generated by said oscillator during apredetermined time interval.

6. Apparatus as recited in claim 5 wherein said means for registeringincludes a digital accumulator; and

means for presetting said accumulator to a negative number equal to thebias of said accelerometer divided by the scale factor of saidaccumulator, said accumulator being reset after a predetermined timeperiod has elapsed, said time period being equal to the reciprocal of MNtimes said scale factor.

7. The apparatus as recited in claim 6 wherein said vibrating stringaccelerometer has a double string configuration in which each of thestring output frequencies is multiplied M and subsequently heterodynedto produce a difference frequency which is proportional to the localgravitational field sensed.

1. Apparatus for removing short term frequency variations in the output signal from an accelerometer which is subjected to both steady and short term accelerations, which accelerometer is of the type which generates an electrical signal having an instantaneous frequency proportional to the acceleration to which it is subjected, comprising: phase detection means having one of two input circuits coupled to the output of said accelerometer and having an output circuit at which is generated a signal having an amplitude proportional to the phase difference between any pair of signals coupled to said input circuits; an oscillator whose frequency is initially set to the mean frequency of said accelerometer and is variable about said mean frequency in response to the amplitude of a control voltage applied to a control circuit thereof, the output of said oscillator being coupled to the other input circuit of said phase detection means; and means connected between the output circuit of said phase detection means and the control circuit of said oscillator for coupling only low frequency components of the signal generated by said phase detection means to said oscillator, whereby the frequency of said oscillator is proportional only to the steady accelerations to which said accelerometer is subjected.
 2. Apparatus for providing an electrical signal whose frequency is a predetermined multiple of the frequency of that component of the output signal from a vibrating string accelerometer generated by the local gravitational field to which said accelerometer is subjected, comprising: a phase detector having one of its two inputs coupled to the output of said accelerometer and having an output circuit at which is generated a signal having an amplitude proportional to the phase difference between any pair of signals coupled to said inputs; a voltage controlled oscillator having a center frequency equal to a predetermined multiple of the mean frequency of the output signal from said accelerometer and having a control circuit which varies the output frequency of said oscillator about said center frequency in response to the amplitude of a control voltage applied thereto; a low-pass filter; means for connecting said low-pass filter between the output circuit of said detector and the voltage control circuit of said oscillator, whereby only low frequency components of the signal from said detector are coupled to said oscillator; means coupled to the output of said oscillator for producing a signal which has a frequency exactly equal to the frequency of said oscillator divided by said predetermined multiple; and means for coupling said last-mentioned signal to the other input of said phase detector so as to provide said detector with a second input signal in addition to that supplied by said accelerometer, whereby the signal available at the output of said oscillator has a frequency which is proportional only to said local gravitational acceleration.
 3. A system for processing signals generated by a vibrating string accelerometer and for determining the strength of the gravitational field to which said accelerometer is subjected, comprising: a phase detector having one of its two inputs coupled to the output of said accelerometer so as to provide said detector with a first input signal and having an output at which is proviDed a signal whose amplitude represents the phase difference between any pair of signals coupled to said inputs; a voltage controlled oscillator for producing a pulsed output signal having a center frequency equal to N times the mean frequency of the output signal from said accelerometer where N is a predetermined positive integer and having a control circuit which varies the output frequency of said oscillator about said center frequency in response to the amplitude of a control voltage applied thereto; means coupled to the output of said oscillator for producing a signal at its output which has a frequency exactly equal to the frequency of said oscillator divided by N; means for coupling the output of said last-mentioned means to the other input of said phase detector so as to provide said detector with a second input signal; a low-pass filter for attenuating the high frequency components of the signal generated at the output of said phase detector; means for connecting said low-pass filter between the output of said detector and the control circuit of said oscillator whereby only low frequency components of the signal from said detector are coupled to said oscillator; and means for registering the number of output pulses generated by said oscillator during a predetermined time interval, whereby said number is proportional to the gravitational field to which said accelerometer is subjected.
 4. The apparatus as recited in claim 3 wherein said registering means includes: a digital accumulator preset to a negative number equal to the bias of said accelerometer divided by the scale factor of said accelerometer; and means for periodically resetting said accumulator after a time period equal to the reciprocal of N times said scale factor has elapsed, whereby the number accumulated in said accumulator during said time period is equal to the gravitational acceleration to which said accelerometer is subjected.
 5. A system for measuring local gravitational accelerations at sea comprising: a vibrating string accelerometer which generates a first signal having a frequency proportional to accelerations to which it is subjected; means for multiplying the frequency of said signal by a positive integer, M, so as to produce a second signal M times greater in frequency than said first signal; a phase detector having one of its two inputs coupled to the output of said multiplying means and having an output which provides a signal whose amplitude represents the phase difference between signals coupled to said inputs; a voltage controlled oscillator having a center frequency N times the mean frequency output of said multiplying means and having a control circuit which varies the output frequency of said oscillator about said center frequency in response to the amplitude of a control voltage applied thereto; a low-pass filter; means for connecting said low-pass filter between the output of said detector and the control circuit of said oscillator so as to complete a feedback loop to said oscillator which loop contains only low frequency components of the signal from said detector; divide-by-N means coupled between the output of said oscillator and the other input of said detector to provide said detector with a signal whose frequency corresponds to that component of the frequency of said second signal due only to gravitational accelerations; and means coupled to the output of said oscillator for registering the number of oscillations generated by said oscillator during a predetermined time interval.
 6. Apparatus as recited in claim 5 wherein said means for registering includes a digital accumulator; and means for presetting said accumulator to a negative number equal to the bias of said accelerometer divided by the scale factor of said accumulator, said accumulator being reset after a predetermined time period has elapsed, said time period being equal to the reciprocal of MN times said scale factor.
 7. The apparatus as recited in claim 6 wherein said vibrating string accelerometer has a double string configuration in which each of the string output frequencies is multiplied M and subsequently heterodyned to produce a difference frequency which is proportional to the local gravitational field sensed. 